Can't receive SMS without an internet connection because of iMessage?

Hello there, MG54321.

It sounds like your'e not receiving messages on your iPhone from other iPhone users. The following Knowledge Base article offers up some great recommendations for troubleshooting:

If you can‘t send or receive messages on your iPhone, iPad, or iPod touch

If your messages aren't sending, or you aren't getting messages

Check your contact information:

1. Make sure that you're using the right phone number or email address for the contact.
2. Go to Settings > Messages > Blocked and make sure that the contact isn't on your block list.

If messages won't send to a certain person or you need help with group messages

Sometimes your messages won't send to a particular contact, or you might have issues with group messages. For example, you might reply to a group conversation and receive your own message. Or you might get a new phone number and see your old one listed as a recipient in an existing group conversation.

Delete the conversation* that has the issue and start a new conversation:

1. Open Messages and look at your list of conversations.
2. Swipe from right to left on the conversation you want to delete. Then tap Delete.
3. Open Messages, tap , and enter the phone number or email address of your contact or contacts.
4. Write a new message and tap send.

*When you delete a conversation, you won’t be able to recover it. If you want to save parts of conversations or their attachments, you can take screenshots. You can also touch and hold an attachment or message bubble, then tap More > Save.

Restart your device and check for updates

1. Restart your device.
2. Check for a carrier settings update.
3. Check for an iOS software update.

Thanks for reaching out to Apple Support Communities.

Cheers.

What does iMessage have to do with it, SMS (texts) do not need or use WiFi.